How do you solve this problem Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. Let C be the event that at least?

To solve this problem, we can analyze the situation using probability. Let ( C ) represent the event that at least one door is unlocked. Since each door can be independently locked or unlocked, we can calculate the total number of combinations of the doors (which is ( 2^3 = 8 )). To find the probability of event ( C ), we can instead calculate the probability of the complementary event (all doors locked) and subtract it from 1. The probability of all three doors being locked is ( \frac{1}{8} ), so the probability of event ( C ) (at least one door is unlocked) is ( 1 - \frac{1}{8} = \frac{7}{8} ).